/*************************************************************************
Cephes Math Library Release 2.8:  June, 2000
Copyright by Stephen L. Moshier

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from C to
      pseudocode.

See subroutines comments for additional copyrights.

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

using System;

namespace alglib
{
    public class gammafunc
    {
        /*************************************************************************
        Gamma function

        Input parameters:
            X   -   argument

        Domain:
            0 < X < 171.6
            -170 < X < 0, X is not an integer.

        Relative error:
         arithmetic   domain     # trials      peak         rms
            IEEE    -170,-33      20000       2.3e-15     3.3e-16
            IEEE     -33,  33     20000       9.4e-16     2.2e-16
            IEEE      33, 171.6   20000       2.3e-15     3.2e-16

        Cephes Math Library Release 2.8:  June, 2000
        Original copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
        Translated to AlgoPascal by Bochkanov Sergey (2005, 2006, 2007).
        *************************************************************************/
        public static double gamma(double x)
        {
            double result = 0;
            double p = 0;
            double pp = 0;
            double q = 0;
            double qq = 0;
            double z = 0;
            int i = 0;
            double sgngam = 0;

            sgngam = 1;
            q = Math.Abs(x);
            if( (double)(q)>(double)(33.0) )
            {
                if( (double)(x)<(double)(0.0) )
                {
                    p = (int)Math.Floor(q);
                    i = (int)Math.Round(p);
                    if( i%2==0 )
                    {
                        sgngam = -1;
                    }
                    z = q-p;
                    if( (double)(z)>(double)(0.5) )
                    {
                        p = p+1;
                        z = q-p;
                    }
                    z = q*Math.Sin(Math.PI*z);
                    z = Math.Abs(z);
                    z = Math.PI/(z*gammastirf(q));
                }
                else
                {
                    z = gammastirf(x);
                }
                result = sgngam*z;
                return result;
            }
            z = 1;
            while( (double)(x)>=(double)(3) )
            {
                x = x-1;
                z = z*x;
            }
            while( (double)(x)<(double)(0) )
            {
                if( (double)(x)>(double)(-0.000000001) )
                {
                    result = z/((1+0.5772156649015329*x)*x);
                    return result;
                }
                z = z/x;
                x = x+1;
            }
            while( (double)(x)<(double)(2) )
            {
                if( (double)(x)<(double)(0.000000001) )
                {
                    result = z/((1+0.5772156649015329*x)*x);
                    return result;
                }
                z = z/x;
                x = x+1.0;
            }
            if( (double)(x)==(double)(2) )
            {
                result = z;
                return result;
            }
            x = x-2.0;
            pp = 1.60119522476751861407E-4;
            pp = 1.19135147006586384913E-3+x*pp;
            pp = 1.04213797561761569935E-2+x*pp;
            pp = 4.76367800457137231464E-2+x*pp;
            pp = 2.07448227648435975150E-1+x*pp;
            pp = 4.94214826801497100753E-1+x*pp;
            pp = 9.99999999999999996796E-1+x*pp;
            qq = -2.31581873324120129819E-5;
            qq = 5.39605580493303397842E-4+x*qq;
            qq = -4.45641913851797240494E-3+x*qq;
            qq = 1.18139785222060435552E-2+x*qq;
            qq = 3.58236398605498653373E-2+x*qq;
            qq = -2.34591795718243348568E-1+x*qq;
            qq = 7.14304917030273074085E-2+x*qq;
            qq = 1.00000000000000000320+x*qq;
            result = z*pp/qq;
            return result;
            return result;
        }


        /*************************************************************************
        Natural logarithm of gamma function

        Input parameters:
            X       -   argument

        Result:
            logarithm of the absolute value of the Gamma(X).

        Output parameters:
            SgnGam  -   sign(Gamma(X))

        Domain:
            0 < X < 2.55e305
            -2.55e305 < X < 0, X is not an integer.

        ACCURACY:
        arithmetic      domain        # trials     peak         rms
           IEEE    0, 3                 28000     5.4e-16     1.1e-16
           IEEE    2.718, 2.556e305     40000     3.5e-16     8.3e-17
        The error criterion was relative when the function magnitude
        was greater than one but absolute when it was less than one.

        The following test used the relative error criterion, though
        at certain points the relative error could be much higher than
        indicated.
           IEEE    -200, -4             10000     4.8e-16     1.3e-16

        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
        Translated to AlgoPascal by Bochkanov Sergey (2005, 2006, 2007).
        *************************************************************************/
        public static double lngamma(double x,
            ref double sgngam)
        {
            double result = 0;
            double a = 0;
            double b = 0;
            double c = 0;
            double p = 0;
            double q = 0;
            double u = 0;
            double w = 0;
            double z = 0;
            int i = 0;
            double logpi = 0;
            double ls2pi = 0;
            double tmp = 0;

            sgngam = 1;
            logpi = 1.14472988584940017414;
            ls2pi = 0.91893853320467274178;
            if( (double)(x)<(double)(-34.0) )
            {
                q = -x;
                w = lngamma(q, ref tmp);
                p = (int)Math.Floor(q);
                i = (int)Math.Round(p);
                if( i%2==0 )
                {
                    sgngam = -1;
                }
                else
                {
                    sgngam = 1;
                }
                z = q-p;
                if( (double)(z)>(double)(0.5) )
                {
                    p = p+1;
                    z = p-q;
                }
                z = q*Math.Sin(Math.PI*z);
                result = logpi-Math.Log(z)-w;
                return result;
            }
            if( (double)(x)<(double)(13) )
            {
                z = 1;
                p = 0;
                u = x;
                while( (double)(u)>=(double)(3) )
                {
                    p = p-1;
                    u = x+p;
                    z = z*u;
                }
                while( (double)(u)<(double)(2) )
                {
                    z = z/u;
                    p = p+1;
                    u = x+p;
                }
                if( (double)(z)<(double)(0) )
                {
                    sgngam = -1;
                    z = -z;
                }
                else
                {
                    sgngam = 1;
                }
                if( (double)(u)==(double)(2) )
                {
                    result = Math.Log(z);
                    return result;
                }
                p = p-2;
                x = x+p;
                b = -1378.25152569120859100;
                b = -38801.6315134637840924+x*b;
                b = -331612.992738871184744+x*b;
                b = -1162370.97492762307383+x*b;
                b = -1721737.00820839662146+x*b;
                b = -853555.664245765465627+x*b;
                c = 1;
                c = -351.815701436523470549+x*c;
                c = -17064.2106651881159223+x*c;
                c = -220528.590553854454839+x*c;
                c = -1139334.44367982507207+x*c;
                c = -2532523.07177582951285+x*c;
                c = -2018891.41433532773231+x*c;
                p = x*b/c;
                result = Math.Log(z)+p;
                return result;
            }
            q = (x-0.5)*Math.Log(x)-x+ls2pi;
            if( (double)(x)>(double)(100000000) )
            {
                result = q;
                return result;
            }
            p = 1/(x*x);
            if( (double)(x)>=(double)(1000.0) )
            {
                q = q+((7.9365079365079365079365*0.0001*p-2.7777777777777777777778*0.001)*p+0.0833333333333333333333)/x;
            }
            else
            {
                a = 8.11614167470508450300*0.0001;
                a = -(5.95061904284301438324*0.0001)+p*a;
                a = 7.93650340457716943945*0.0001+p*a;
                a = -(2.77777777730099687205*0.001)+p*a;
                a = 8.33333333333331927722*0.01+p*a;
                q = q+a/x;
            }
            result = q;
            return result;
        }


        private static double gammastirf(double x)
        {
            double result = 0;
            double y = 0;
            double w = 0;
            double v = 0;
            double stir = 0;

            w = 1/x;
            stir = 7.87311395793093628397E-4;
            stir = -2.29549961613378126380E-4+w*stir;
            stir = -2.68132617805781232825E-3+w*stir;
            stir = 3.47222221605458667310E-3+w*stir;
            stir = 8.33333333333482257126E-2+w*stir;
            w = 1+w*stir;
            y = Math.Exp(x);
            if( (double)(x)>(double)(143.01608) )
            {
                v = Math.Pow(x, 0.5*x-0.25);
                y = v*(v/y);
            }
            else
            {
                y = Math.Pow(x, x-0.5)/y;
            }
            result = 2.50662827463100050242*y*w;
            return result;
        }
    }
}
